The mathematical brain — how children learning counting numbers

 Counting is easy to take for granted, but there is a lot of intriguing literature into how we learning counting numbers, and there is more to it than you would expect.

The brain in mathematics

First of all, it’s worth remembering where our mathematical talent comes from.

In his book “The Mathematical Brain,” neuropsychologist Brian Butterworth argues that we are born with an inherent sense of number hard-wired into our brain and he attributes this to a small brain area behind the left ear he calls “the number module.” He contrasts this definition to color-the “twoness” or “Threeness” of a set of objects can often be viewed in the same manner we interpret the “greenness” of a leaf.

Keep counting. We like to assume, like times tables and arithmetic, that it’s something children ought to be taught. Wrong, Butterworth says — that’s an impulse. Yes, to establish that instinct, we have to study the names and symbols of numbers, however, since the number module is hardwired into the brain, simple counting comes easily.

Even though they have no vocabulary for numbers, distant tribes will count. In math, as in words, he claims, “kids start off with little starter kits” and the number module is their math starter kit.

There are also other hypotheses, such as math being an extension of our spatial knowledge, but in the notion of a “little math starter kit” there is something sweet.

All this does not mean that a child is predestined to either be good at math or not. A word of caution. We’re not born eager to study algebra, far from it, and it’s what takes place in the first 10 years or so that sets us up.

Data shows that children, even as young as 12 months of age, have a sense of how many items are in a group, up to around three. This stems from the inherent sense of number in them.

Counting is mastered as the toddler begins to associate this intuitive sense of “how many there are” with the vocabulary that we use to count “one, two, buckle my shoe” In learning algebra, this is the first step and it is the building stone for many early concepts.

Will parents have their babies counted on? Definitely, using a selection of actual things. And it is as, if not more, necessary to read to your children because counting and language are interlinked.

Counting — milestones from early learning

Here are several stages of learning to count that you might find your child going through at ages 3 to 5: Knowing without counting how many items are in a small set. So, if you show your kid four apples, they’re not going to have to count them in order to convince you that there are four.

Knowing the words “number words” and their order from one to ten.

No matter what number they start on, know the chain. As compared to starting from one at all times.

Quantity retention — This is when children know that until others are added or eliminated, the number of objects in a collection remains the same. So, if six cans of beans are numbered in a straight line, then you rearrange the beans (in front of their eyes) into two stacks of three, they’ll know that without counting, there are already six.

Counting non-visible objects — the infant can know that they can count items that they cannot touch or even see, such as sounds, family members of someone else, or even emotions.

This is to realize that the last number counted is equal to the sum of the set. Cardinality, not to be confused with carnality. If your child has six 1,2,3,4,5,6 oranges and you inquire “how many oranges are there” then? And they count them again, then “cardinality” they have not understood.

Counting on — as a step to the addition of

As an extension of counting, learning to add comes. To make this relation, here are several stages a child goes through:

Counting all — For 3 + 5, children will count “one, two, three” and then “one, two, three, four, five” to decide the number of sets to be included, such as three fingers on one side and five fingers on the other. The kid will then count all “one, two, three, four, five, six, seven, eight” items

Counting on the first number — Some children know that the first number to be added doesn’t need to be counted. To get the solution, they can begin with three, and then count on another five. The child would no longer count out the first set using finger counting, but begin with the word ‘Three’ and then use a hand to count on the second added: ‘Four, five, six, seven, eight.’

Counting on the greater number — When the smaller of the two numbers is counted, it is more accurate. The child now selects “five” as the largest number to begin with, and then counts “six, seven, eight”

The final step does not really count — it is where learners know their number of facts and totally miss the time-consuming counting.

Number lines are wonderful visual resources — we use them a lot in Komodo to render this relation between “counting on” and addition or subtraction. Here’s an earlier blog post all about lines of numbers.

Beyond fundamental counting

Counting is the first meeting for mathematical pattern learners. They will soon start counting backwards from here, which is a step towards subtraction, and they will also count in twos, fives, and tens, which are the basis for multiplication.

The principle of location meaning and counting to base 10 is the next major step. This jump is often taken by learners precisely because it’s an obvious and easy method of measuring huge numbers. In Komodo, we use examples of experience like this to help learners render the connection to tens and tens of counting.

It is easy to forget that counting in mathematics is a core concept with several steps before it is perfected. Certainly, there is a lot more to it than one, two, three!

Source: The Soft Roots